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Finished re-writing lab 1. Getting started guide introduces variables, functions, and logic

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Adog64
2025-01-19 03:01:16 -05:00
parent 6d2257bbf8
commit ee51f180d4
10 changed files with 159 additions and 54 deletions
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4
8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q3.m
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@@ -1,2 +1,2 @@
syms t
a=simplify(fourier(sin(0.5*t)/(0.5*t)))
syms t % Define t as a symbolic variable
a=simplify(fourier(sin(0.5*t)/(0.5*t))) % Print the simplified Fourier transform of sin(0.5t)/(0.5t) = sinc(0.5t)

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q3.py
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@@ -3,45 +3,18 @@ ECE 09351 - Digital Signal Processing
Lab 1 Question 3
Translated from MATLAB by Aidan Sharpe
Last Modified: January 17, 2025
Last Modified: January 18, 2025
"""
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
def cft(g, f):
result = np.zeros(len(f), dtype=complex)
for i, ff in enumerate(f):
result[i] = complex_quad(lambda t: g(t)*np.exp(-2j*np.pi*ff*t), -5, 5)
return result
def complex_quad(g, a, b):
t = np.linspace(a, b, 2501)
x = g(t)
return sp.integrate.simpson(y=x, x=t)
from sympy import simplify, fourier_transform, sinc
from sympy.abc import t, f
def main():
g = lambda t: np.sinc(0.5*t/np.pi)
f_s = 1
T_s = 1/f_s
t_0 = 1000
t = np.arange(-t_0, t_0, T_s)
f = np.linspace(-f_s/2, f_s/2, len(t), endpoint=False)
omega = 2*np.pi*f
G = np.fft.fftshift(np.fft.fft(g(t)) * np.exp(-2j*np.pi*f*t_0) /f_s)
G_analytic = 2*np.pi*(np.heaviside(omega+0.5, 1) - np.heaviside(omega-0.5, 1))
plt.plot(f, G_analytic, color="red")
plt.scatter(f, G)
plt.show()
x = sinc(0.5*t) # Define x as sinc(0.5t) = sin(0.5t)/(0.5t)
X = simplify(fourier_transform(x, t, f)) # Evaluate the Fourier transform of x, converting from t domain to f domain
print(X)
if __name__ == "__main__":

8
8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q4.m
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@@ -1,12 +1,12 @@
% Lab 1
% Question 4
fs=4;
ts=1/fs;
fs=4; % Sample frequency 4[Hz]
ts=1/fs; % Period is reciprocal of frequency
n=0:1:99;
n=0:1:99; % Sample indicies (0 to 99)
x(n+1)=cos(2*pi*n*ts/5)+sin(4*pi*n*ts/7)+cos(16*pi*n*ts/9);
stem(n,x,'linewidth',2);
stem(n,x,'linewidth',2); % Plot samples on stem plot
xlabel('n')
ylabel('x(n)')

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q4.py Normal file
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@@ -0,0 +1,30 @@
"""
ECE 09351 - Digital Signal Processing
Lab 1 Question 4
Translated from MATLAB by Aidan Sharpe
Last Modified: January 18, 2025
"""
import numpy as np
import matplotlib.pyplot as plt
def main():
f_s = 4 # Sample frequency 4[Hz]
T_s = 1/f_s # Period is reciprocal of frequency
n = np.arange(100) # Sample indicies (0 to 99)
t = n*T_s # Conversion between index and time
x = np.cos(2*np.pi*t/5) + np.sin(4*np.pi*t/7) + np.cos(16*np.pi*t/9)
plt.stem(n, x) # Plot samples against index on stem plot
plt.xlabel("n")
plt.ylabel("x(n)")
plt.show() # Show the plot
if __name__ == "__main__":
main()

6
8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q5.m
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@@ -1,3 +1,3 @@
syms t
f=exp(-t*4)*heaviside(t);
ff=fourier(f);
syms t % Define t as a symbolic variable
f=exp(-t*4)*heaviside(t); % Define f(t) = e^(-4t)*u(t)
ff=fourier(f); % Take the Fourier transform of f(t)

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q5.py Normal file
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@@ -0,0 +1,19 @@
"""
ECE 09351 - Digital Signal Processing
Lab 1 Question 5
Translated from MATLAB by Aidan Sharpe
Last Modified: January 18, 2025
"""
from sympy import fourier_transform, exp, Q
from sympy.abc import t, f
def main():
x = exp(-4*t)*Heaviside(t) # Define x(t) = e^(-4t)*u(t)
X = fourier_transform(x, t, f) # Take the Fourier transform of x(t)
print(x)
if __name__ == "__main__":
main()

15
8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q6.m
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@@ -1,9 +1,8 @@
syms a b t
assume(a > 0)
f = exp(-a*abs(t));
ff = fourier(f);
assume(b > 0)
g = f*cos(b*t);
gg = simplify(fourier(g));
syms a b t % Define a, b, and t as symbolic variables
assume(a > 0) % Assume a is a positive real number
f = exp(-a*abs(t)); % Define f(t) = e^(-a|t|)
ff = fourier(f) % Take the Fourier transform of f(t)
assume(b > 0) % Assume b is a positive real number
g = f*cos(b*t); % Define g(t) = e^(-a|t|)*cos(bt)
gg = simplify(fourier(g)) % Take the Fourier transform of g(t)

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q6.py Normal file
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@@ -0,0 +1,29 @@
"""
ECE 09351 - Digital Signal Processing
Lab 1 Question 6
Translated from MATLAB by Aidan Sharpe
Last Modified: January 18, 2025
"""
from sympy import *
from sympy.abc import a, b, t, w
# Please note that the answers are given as piecewise functions.
# The conditions are unnecessary, so take the first part of the piecewise result.
def main():
# Assume that a and b are positive real numbers
with assuming(Q.positive(a), Q.positive(b)):
x_1 = exp(-a*abs(t)) # x1(t) = e^(-a|t|)
X_1 = integrate(x_1*exp(-1j*w*t), (t, -oo, oo)) # Fourier transform of x1(t)
print(simplify(X_1))
x_2 = x_1*cos(b*t) # x2(t) = x1(t)*cos(bt)
X_2 = integrate(x_2*exp(-1j*w*t), (t, -oo, oo)) # Fourier transform of x2(t)
print(simplify(X_2))
if __name__ == "__main__":
main()